Finite Group Databasebeta

← C31×#8490 #21465249

Subgroups — C31×#8490 #21465249

Order 7936.

630 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3564C211yesmaximal, characteristic
2C31×#1554C211yesmaximal, characteristic, complemented
3C31×#1535C211yesmaximal, characteristic, complemented
4C31×#1497C211yesmaximal, characteristic, complemented
5C31×#1482C211yesmaximal, characteristic, complemented
6C31×#1473C211yesmaximal, characteristic, complemented
7C31×#1473C211yesmaximal, characteristic, complemented
8C31×#563—21no—
9C31×#563—21no—
10C31×#556—21no—
11C31×#554—21no—
12C31×#552—21no—
13C31×#552—21no—
14C31×#551—21no—
15C31×#551—21no—
16C31×#544C411yescharacteristic
17C31×#543C411yescharacteristic
18C31×#542—21no—
19C31×#541—21no—
20C31×#541—21no—
21C31×#539—21no—
22C31×#539C411yescharacteristic
23C31×#538C411yescharacteristic
24C31×#533C2211yescharacteristic
25C31×#529C2211yescharacteristic
26C2×C31×#126C2211yescharacteristic
27C31×#432C2211yescharacteristic
28C31×#432C2211yescharacteristic
29C31×#431C2211yescharacteristic
30C31×#431C2211yescharacteristic
31C31×#333—21no—
32C31×#332—21no—
33C31×#330—21no—
34C31×#329—21no—
35C31×Q8⋊C8—21no—
36C31×Q8⋊C8—21no—
37C31×Q8⋊C8—21no—
38C31×D4⋊C8—21no—
39C31×#324—21no—
40C31×#324—21no—
41C31×#323—21no—
42C31×#323—21no—
43C31×C4⋊Q8—21no—
44C31×C4⋊Q8—21no—
45C31×C4⋊Q8—21no—
46C31×C4⋊Q8D411yescharacteristic
47C31×C4⋊Q8D411yescharacteristic
48C31×#126—21no—
49C31×#126—21no—
50C31×#126—21no—
51C31×#126—21no—
52C31×#126—21no—
53C31×#126—21no—
54C31×#126—21no—
55C31×#126—21no—
56C31×#126—21no—
57C31×#126—21no—
58C31×#126—21no—
59C31×#126—21no—
60C31×#126—21no—
61C31×#125—21no—
62C31×#125—21no—
63C31×#125—21no—
64C31×#125—21no—
65C31×#125—21no—
66C31×#125—21no—
67C31×#125—21no—
68C31×#125—21no—
69C31×#125—21no—
70C31×#125D411yescharacteristic
71C31×#124—21no—
72C31×#124—21no—
73C31×#124—21no—
74C31×#124D411yescharacteristic
75C31×#123—21no—
76C31×#123—21no—
77C31×#123—21no—
78C31×#123—21no—
79C31×#123—21no—
80C31×#123—21no—
81C31×#123—21no—
82C31×#123—21no—
83C31×C22⋊Q8—21no—
84C31×C22⋊Q8—21no—
85C31×C22⋊Q8—21no—
86C31×C22⋊Q8—21no—
87C31×C22⋊Q8—21no—
88C31×C22⋊Q8—21no—
89C31×C22⋊Q8—21no—
90C31×C22⋊Q8—21no—
91C31×C22⋊Q8—21no—
92C31×C22⋊Q8—21no—
93C31×C22⋊Q8—21no—
94C31×C22⋊Q8—21no—
95C31×C22⋊Q8—21no—
96C31×C22⋊Q8—21no—
97C31×C22⋊Q8C2×C411yescharacteristic
98C31×C22⋊Q8C2×C411yescharacteristic
99C31×C22⋊Q8C2×C411yescharacteristic
100C31×#121—21no—
101C31×#121C2×C411yescharacteristic
102C31×#120—21no—
103C4×Q8×C31—21no—
104C4×Q8×C31—21no—
105C4×Q8×C31—21no—
106C4×Q8×C31D411yescharacteristic
107C4×Q8×C31D411yescharacteristic
108C4×Q8×C31D411yescharacteristic
109C4×D4×C31—21no—
110C4×D4×C31—21no—
111C4×D4×C31—21no—
112C4×D4×C31—21no—
113C4×D4×C31—21no—
114C4×D4×C31D411yescharacteristic
115C31×#117—21no—
116C31×#117—21no—
117C31×#117—21no—
118C31×#117—21no—
119C31×#117—21no—
120C31×#117—21no—
121C2×C4⋊C4×C31—21no—
122C2×C4⋊C4×C31C2×C411yescharacteristic
123C2×C4⋊C4×C31D411yescharacteristic
124C2×C4⋊C4×C31D411yescharacteristic
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31C2×C411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C42×C31C2311yescharacteristic
130C31×C4⋊C8—21no—
131C31×C4⋊C8—21no—
132C31×C4⋊C8—21no—
133C31×C4⋊C8—21no—
134C31×C22⋊C8—21no—
135C31×C22⋊C8—21no—
136C31×C22⋊C8—21no—
137C31×C22⋊C8—21no—
138C31×#97—21no—
139C31×#97—21no—
140C4×C8×C31—21no—
141C4×C8×C31—21no—
142C24×C31C22⋊C411yescharacteristic
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31C22⋊C411yescharacteristic
147C2×Q8×C31C22⋊C411yescharacteristic
148C2×Q8×C31C22⋊C411yescharacteristic
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31C22⋊C411yescharacteristic
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31C22⋊C411yescharacteristic
159C22×C4×C31C22⋊C411yescharacteristic
160C22×C4×C31C22⋊C411yescharacteristic
161C22×C4×C31C22×C411yescharacteristic
162C22×C4×C31C2×D411yescharacteristic
163C22×C4×C31C2×D411yescharacteristic
164C2×C8×C31—41no—
165C2×C8×C31—41no—
166C2×C8×C31—41no—
167C2×C8×C31—41no—
168C4⋊C4×C31—21no—
169C4⋊C4×C31—21no—
170C4⋊C4×C31—21no—
171C4⋊C4×C31—21no—
172C4⋊C4×C31—21no—
173C4⋊C4×C31—21no—
174C4⋊C4×C31—21no—
175C4⋊C4×C31—21no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—21no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31C22⋊C411yescharacteristic
198C4⋊C4×C31C22⋊C411yescharacteristic
199C4⋊C4×C31C22⋊C411yescharacteristic
200C4⋊C4×C31C22⋊C411yescharacteristic
201C22⋊C4×C31—21no—
202C22⋊C4×C31—21no—
203C22⋊C4×C31—21no—
204C22⋊C4×C31—21no—
205C22⋊C4×C31—21no—
206C22⋊C4×C31—21no—
207C22⋊C4×C31—21no—
208C22⋊C4×C31—21no—
209C22⋊C4×C31—21no—
210C22⋊C4×C31—21no—
211C22⋊C4×C31—21no—
212C22⋊C4×C31—21no—
213C22⋊C4×C31—21no—
214C22⋊C4×C31—21no—
215C22⋊C4×C31—21no—
216C22⋊C4×C31—21no—
217C22⋊C4×C31—21no—
218C22⋊C4×C31—21no—
219C22⋊C4×C31—21no—
220C22⋊C4×C31—21no—
221C22⋊C4×C31—21no—
222C42×C31—21no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—21no—
227C42×C31—21no—
228C42×C31—21no—
229C42×C31C2×D411yescharacteristic
230C42×C31C2×D411yescharacteristic
231C42×C31C2×D411yescharacteristic
232C42×C31C2×D411yescharacteristic
233#8490C3111yesmaximal, characteristic, direct product factor, Sylow
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31C2×C22⋊C411yescharacteristic
240Q8×C31—41no—
241Q8×C31—41no—
242Q8×C31—41no—
243Q8×C31—81no—
244Q8×C31—81no—
245Q8×C31—81no—
246D4×C31—41no—
247D4×C31—42no—
248D4×C31—81no—
249D4×C31—81no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—81no—
267C2×C4×C31—81no—
268C2×C4×C31—81no—
269C2×C4×C31—81no—
270C2×C4×C31—81no—
271C2×C4×C31C2×C22⋊C411yescharacteristic
272C2×C4×C31C2×C22⋊C411yescharacteristic
273C2×C4×C31#12011yescharacteristic
274C2×C4×C31#12011yescharacteristic
275C2×C4×C31#12011yescharacteristic
276C2×C4×C31#12011yescharacteristic
277C8×C31—81no—
278C8×C31—81no—
279C8×C31—81no—
280C8×C31—81no—
281#3564C2×C3111yescharacteristic
282#1554C2×C3111yescharacteristic, complemented
283#1535C2×C3111yescharacteristic, complemented
284#1497C2×C3111yescharacteristic, complemented
285#1482C2×C3111yescharacteristic, complemented
286#1473C2×C3111yescharacteristic, complemented
287#1473C2×C3111yescharacteristic, complemented
288C22×C31—21no—
289C22×C31—21no—
290C22×C31—21no—
291C22×C31—41no—
292C22×C31—41no—
293C22×C31—41no—
294C22×C31—41no—
295C22×C31—41no—
296C22×C31—41no—
297C22×C31—161no—
298C22×C31#37911yescharacteristic
299C4×C31—21no—
300C4×C31—21no—
301C4×C31—21no—
302C4×C31—21no—
303C4×C31—21no—
304C4×C31—21no—
305C4×C31—41no—
306C4×C31—41no—
307C4×C31—41no—
308C4×C31—41no—
309C4×C31—41no—
310C4×C31—41no—
311C4×C31—41no—
312C4×C31—41no—
313C4×C31—41no—
314C4×C31—41no—
315#563—21no—
316#563—21no—
317#556—21no—
318#554—21no—
319#552—21no—
320#552—21no—
321#551—21no—
322#551—21no—
323#544C4×C3111yescharacteristic
324#543C4×C3111yescharacteristic
325#542—21no—
326#541—21no—
327#541—21no—
328#539—21no—
329#539C4×C3111yescharacteristic
330#538C4×C3111yescharacteristic
331#533C22×C3111yescharacteristic
332#529C22×C3111yescharacteristic
333C2×#126C22×C3111yescharacteristic
334#432C22×C3111yescharacteristic
335#432C22×C3111yescharacteristic
336#431C22×C3111yescharacteristic
337#431C22×C3111yescharacteristic
338#333—21no—
339#332—21no—
340#330—21no—
341#329—21no—
342Q8⋊C8—21no—
343Q8⋊C8—21no—
344Q8⋊C8—21no—
345D4⋊C8—21no—
346#324—21no—
347#324—21no—
348#323—21no—
349#323—21no—
350C2×C31—41no—
351C2×C31—81no—
352C2×C31—81no—
353C2×C31#179111yescharacteristic
354C2×C31#179411yescharacteristic
355C2×C31#179611yescharacteristic
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8D4×C3111yescharacteristic
360C4⋊Q8D4×C3111yescharacteristic
361#126—21no—
362#126—21no—
363#126—21no—
364#126—21no—
365#126—21no—
366#126—21no—
367#126—21no—
368#126—21no—
369#126—21no—
370#126—21no—
371#126—21no—
372#126—21no—
373#126—21no—
374#125—21no—
375#125—21no—
376#125—21no—
377#125—21no—
378#125—21no—
379#125—21no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125D4×C3111yescharacteristic
384#124—21no—
385#124—21no—
386#124—21no—
387#124D4×C3111yescharacteristic
388#123—21no—
389#123—21no—
390#123—21no—
391#123—21no—
392#123—21no—
393#123—21no—
394#123—21no—
395#123—21no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410C22⋊Q8C2×C4×C3111yescharacteristic
411C22⋊Q8C2×C4×C3111yescharacteristic
412C22⋊Q8C2×C4×C3111yescharacteristic
413#121—21no—
414#121C2×C4×C3111yescharacteristic
415#120—21no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×Q8—21no—
419C4×Q8D4×C3111yescharacteristic
420C4×Q8D4×C3111yescharacteristic
421C4×Q8D4×C3111yescharacteristic
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4D4×C3111yescharacteristic
428#117—21no—
429#117—21no—
430#117—21no—
431#117—21no—
432#117—21no—
433#117—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4C2×C4×C3111yescharacteristic
436C2×C4⋊C4D4×C3111yescharacteristic
437C2×C4⋊C4D4×C3111yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4C2×C4×C3111yescharacteristic
440C2×C22⋊C4D4×C3111yescharacteristic
441C2×C22⋊C4D4×C3111yescharacteristic
442C2×C42C23×C3111yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8—21no—
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453C4×C8—21no—
454C4×C8—21no—
455C31#849011yescharacteristic, direct product factor, Sylow
456C24C22⋊C4×C3111yescharacteristic
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8C22⋊C4×C3111yescharacteristic
461C2×Q8C22⋊C4×C3111yescharacteristic
462C2×Q8C22⋊C4×C3111yescharacteristic
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4C22⋊C4×C3111yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4C22⋊C4×C3111yescharacteristic
473C22×C4C22⋊C4×C3111yescharacteristic
474C22×C4C22⋊C4×C3111yescharacteristic
475C22×C4C22×C4×C3111yescharacteristic
476C22×C4C2×D4×C3111yescharacteristic
477C22×C4C2×D4×C3111yescharacteristic
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4C22⋊C4×C3111yescharacteristic
512C4⋊C4C22⋊C4×C3111yescharacteristic
513C4⋊C4C22⋊C4×C3111yescharacteristic
514C4⋊C4C22⋊C4×C3111yescharacteristic
515C22⋊C4—21no—
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C22⋊C4—21no—
531C22⋊C4—21no—
532C22⋊C4—21no—
533C22⋊C4—21no—
534C22⋊C4—21no—
535C22⋊C4—21no—
536C42—21no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42C2×D4×C3111yescharacteristic
544C42C2×D4×C3111yescharacteristic
545C42C2×D4×C3111yescharacteristic
546C42C2×D4×C3111yescharacteristic
547C23—21no—
548C23—21no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23C2×C22⋊C4×C3111yescharacteristic
553Q8—41no—
554Q8—41no—
555Q8—41no—
556Q8—81no—
557Q8—81no—
558Q8—81no—
559D4—41no—
560D4—42no—
561D4—81no—
562D4—81no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—81no—
580C2×C4—81no—
581C2×C4—81no—
582C2×C4—81no—
583C2×C4—81no—
584C2×C4C2×C22⋊C4×C3111yescharacteristic
585C2×C4C2×C22⋊C4×C3111yescharacteristic
586C2×C4C31×#12011yescharacteristic
587C2×C4C31×#12011yescharacteristic
588C2×C4C31×#12011yescharacteristic
589C2×C4C31×#12011yescharacteristic
590C8—81no—
591C8—81no—
592C8—81no—
593C8—81no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—161no—
604C22C31×#37911yescharacteristic
605C4—21no—
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C2—41no—
622C2—81no—
623C2—81no—
624C2C31×#179111yescharacteristic
625C2C31×#179411yescharacteristic
626C2C31×#179611yescharacteristic
subgroupG/H
center, socleC22×C31#379
commutatorC22×C4C22×C4×C31
Frattini, cosocleC2×C42C23×C31
prime radicalC31×#538C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C31×#1554C2semidirect
3. C31×#1535C2semidirect
4. C31×#1497C2semidirect
5. C31×#1482C2semidirect
6. C31×#1473C2semidirect
7. C31×#1473C2semidirect
233. #8490C31direct (N × H)
282. #1554C2×C31semidirect
283. #1535C2×C31semidirect
284. #1497C2×C31semidirect
285. #1482C2×C31semidirect
286. #1473C2×C31semidirect
287. #1473C2×C31semidirect
455. C31#8490direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C31×#35642
C31×#15542
C31×#15352
C31×#14972
C31×#14822
C31×#14732
#849031